Mix crushed cookies with melted butter to make the crust. Pat onto the bottom and sides of a 9-inch pie pan.
Heat marshmallows and milk together in a large saucepan over low heat, stirring constantly, until marshmallows are melted, about 8 minutes. Stir in creme de menthe, creme de cacao, and green food coloring until smooth.
Immerse the bottom of the saucepan in cool water for several minutes to cool the marshmallow mixture.
Beat cream in a chilled glass or metal bowl with an electric mixer until soft peaks form. Fold whipped cream into marshmallow mixture. Pour into pie crust and smooth the top.
Cover pie with plastic wrap and freeze until set, about 3 hours.